宁夏大学学报（自然科学版）2018，Vol.39Issue(1)：38-41,47,5.
用同伦摄动法求解第一类超奇异积分方程
Homotopy Perturbation Method for Solving Hypersingular Integral Equations of the First Kind
摘要
Abstract
A large number of physical and engineering problems can be described by hypersingular integral equations,but it is difficult to solve the analytical solutions of such equations.Therefore,researchers have paid their attentions to study the numerical solutions of the hypersingular integral equations.In this paper,the hypersingular integral equation of the first kind is solved by the homotopy perturbation method,and the numerical examples are used to verify the validity of the method.Finally,the method is applied to solve the fracture mechanics problem,and the value of the stress intensity factors of the crack tips is given.The comparison between the numerical solution and the analytical solution shows that the homotopy perturbation method is very effective in solving the fracture mechanics problems with cracks.关键词
同伦摄动法/超奇异积分方程/裂纹/应力强度因子Key words
homotopy perturbation method/hypersingular integral equation/crack/stress intensity factor分类
数理科学引用本文复制引用
汪菊玲,汪文帅..用同伦摄动法求解第一类超奇异积分方程[J].宁夏大学学报（自然科学版）,2018,39(1):38-41,47,5.基金项目
国家自然科学基金资助项目(11561055) （11561055）
